ATREIDES - II. Detection of a polar orbit for HAT-P-26 b, a fluffy planet in the Neptunian ridge

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Table 1

Properties of the HAT-P-26 system.

Parameter	Symbol	Value	Unit	Origin
Stellar parameters: physical parameters
Spectral type		K1 V		Hartman et al. (2011)
Age	τ	${9.0}_{- 4.9}^{+ 3.0}$ $Mathematical equation: $9.0^{+3.0}_{-4.9}$$		Hartman et al. (2011)
Age_[Y/Zn]	τ_[Y/Zn]	11.65 ± 2.16	Gyr	This work (Sect. 4.1)
Age_[Y/Mg]	τ_[Y/Mg]	13.51 ± 2.00		This work (Sect. 4.1)
Age_[Y/Si]	τ_[Y/Si]	14.54 ± 2.36		This work (Sect. 4.1)
Temperature	T_eff	5006 ± 61	K	This work (Sect. 4.1)
Surface gravity	log g_Gaia	4.45 ± 0.05		This work (Sect. 4.1)
Metallicity	[Fe/H] (dex)	−0.023 ± 0.037		This work (Sect. 4.1)
Radius	R_⋆	0.91 ± 0.03	R_⊙	This work (Sect. 4.1)
Mass	M_⋆	0.78 ± 0.01	M_⊙	This work (Sect. 4.1)
Spin inclination	$i_{⋆}^{N}$ $Mathematical equation: $i_{\star}^{\rm N}$$	$25_{- 12}^{+ 12}$ $Mathematical equation: $25_{-12}^{+12}$$		This work
Spin inclination	$i_{⋆}^{S}$ $Mathematical equation: $i_{\star}^{\rm S}$$	$155_{- 12}^{+ 12}$ $Mathematical equation: $155_{-12}^{+12}$$	deg	This work
Projected velocity	v_eq sin i_⋆	${0.23}_{- 0.08}^{+ 0.08}$ $Mathematical equation: $0.23^{+0.08}_{-0.08}$$	km s⁻¹	This work (Sect. 5.4)
Limb-darkening coefficients	u₁	0.53 ± 0.05		This work (Sect. 3)
Limb-darkening coefficients	u₂	0.13 ± 0.05		This work (Sect. 3)

Stellar parameters: chemical abundances

	[Mg/H] (dex)	0.11 ± 0.05		This work (Sect. 4.1)
	[Si/H] (dex)	0.04 ± 0.06		This work (Sect. 4.1)
Chemical abundances	[Ni/H] (dex)	−0.04 ± 0.06		This work (Sect. 4.1)
	[Zn/H] (dex)	−0.04 ± 0.06		This work (Sect. 4.1)
	[Y/H] (dex)	−0.22 ± 0.10		This work (Sect. 4.1)

Planet parameters

Orbital period	P_orb	4.2345002 ± 0.0000006	days	This work (Sect. 3)
Transit epoch	T₀	2459763.5809 ± 0.0008^†	BJD_TDB	This work (Sect. 3)
Orbital inclination	i_p	${87.7}_{- 2.0}^{+ 1.6}$ $Mathematical equation: $87.7^{+1.6}_{-2.0}$$	deg	This work (Sect. 3)
Scaled separation	a/R_⋆	${12.1}_{- 2.1}^{+ 2.0}$ $Mathematical equation: $12.1^{+2.0}_{-2.1}$$		This work (Sect. 3)
Eccentricity	e	${0.13}_{- 0.06}^{+ 0.06}$ $Mathematical equation: $0.13^{+0.06}_{-0.06}$$		This work (Sect. 3)
Argument of periastron	ω	${44.00}_{- 113}^{+ 80}$ $Mathematical equation: $44.00_{-113}^{+80}$$	deg	This work (Sect. 3)
Impact parameter	b	${0.49}_{- 0.32}^{+ 0.25}$ $Mathematical equation: $0.49^{+0.25}_{-0.32}$$		This work (Sect. 3)
Projected spin–orbit angle	λ	$- 78_{- 13}^{+ 13}$ $Mathematical equation: $-78_{-13}^{+13}$$	deg	This work (Sect. 5.4)
3D spin–orbit angle	ψ^N	$84_{- 5}^{+ 5}$ $Mathematical equation: $84_{-5}^{+5}$$
	ψ^S	$86_{- 5}^{+ 5}$ $Mathematical equation: $86_{-5}^{+5}$$	deg	This work (Sect. 5.4)
	ψ	$85_{- 5}^{+ 5}$ $Mathematical equation: $85_{-5}^{+5}$$
Stellar reflex velocity	K	8.5 ± 1.0	ms⁻¹	Hartman et al. (2011)
Planet mass	M_p	18.75 ± 2.23	M_⊕	Hartman et al. (2011)
Transit duration	T₁₄	2.4552 ± 0.024	hours	Hartman et al. (2011)
Planet radius	R_p	${6.33}_{- 0.36}^{+ 0.81}$ $Mathematical equation: $6.33^{+0.81}_{-0.36}$$	R_⊕	Hartman et al. (2011)

Notes. ^†A constant-period ephemeris was adopted for all the analyses. Since the TTV amplitude is ∼2 minutes (A-thano et al. 2023), it should not significantly affect our results (see also Appendix F).

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